The invention is directed to providing systems capable of emulating the regulatory and developmental characteristics that are found in living organisms which are thermodynamically-open, nutritionally-influenced systems. Those versed in systems theory will appreciate that thermal and other initializing energy-disturbances or conditions can be fully- or partially-propagated by a closed-loop regulatory system of complex organisms, which ironically can preclude their development from being optimal. The present system incorporates means for determining a singular component that may be found in certain natural phenomena and means for determining a recursive component that may be found in other natural phenomena and the combination of these two components provides utility as a generic model for evaluation, estimation, and control purposes of various physio-chemical processes.
One open system to which the present invention is applicable is in the postnatal feeding of infants resulting in weight increase thereof. During postnatal feeding, there is an open thermodynamic system in which food intake is reflected by anticipated weight gain, whereas in adulthood energy input is sustaining of weight.
Other open-systems to which the present invention is applicable include complex electrical, mechanical or chemical systems such as coupled processes in power-generating systems, flow processes, and other time-varying networks that may be analyzed and stabilized by using Lyapunov (generalized energy) functions.
The present invention provides a method applicable to this class of techniques which, in their "dynamic programming" form, are considered to be intelligent, in that they are directed toward a long-term goal. The Riccati equation is a special linear-quadratic case that is widely employed in control theory to determine optimal feedback parameters for linear systems. In contrast, the present method represents a non-linear multiplicative form, also known as a bilinear functional factor. Unlike conventional dynamic programming, it does not impose or require asymptotic stability, but only nominal "vibrational" stationarity which more realistically represents the behavior of actual physical systems, which often display periodicity or "limit-cycles". Moreover, the nominal steady-state attained may be independent of the initial condition(s), as a result of the controlling or perturbing effect of time-varying "dissipative" groups of multiplicative feedback parameters. In other words, the invention is concerned with a process which allows transient instability as a means of compensating for disturbances, and effectively "diffuses" or dissipates the undesired conditions. This is a known property of open-systems which is retained in the present invention by incorporating open-system "energy" parameters therein. Also, whereas conventional dynamic programming relies upon a backward flow of information from the desired final condition(s), the present method is capable of operating in a feed-forward mode, and thereby can control the operation of a nonlinear, non-stationary stochastic-process, in which neither steady-state conditions, nor viable trajectories can be specified at the outset, though these may be fortuitously estimated by the present invention as more data pertinent to the process becomes available. Hence, the present invention is particularly capable of tracking self-organizing or otherwise adaptive, goal-directed, or autonomous processes, including growth, diffusion, and fractional Brownian-motion.
Other applications of the present invention include image-processing and pattern recognition. In application to a static image, time is replaced by two space variables, or one complex variable. Alternatively, processing can be carried out on a video (scanned) time-signal. In pattern recognition and "neuro" computation applications, the invention is employed in conjunction with appropriate (statistical) decision criteria, and the like.